This invention relates to MEMS resonators.
MEMS resonators are used in reference oscillators in RF receiver circuits. The resonance frequency of a MEMS resonator in silicon exhibits a temperature drift of typically −30 ppm/K. For some applications this drift needs to be reduced significantly. For example, when using a MEMS resonator in a GSM reference oscillator the drift needs to be below +/−20 ppm or even +/−10 ppm over a temperature range of 100K.
This can be achieved by keeping the resonator at a constant temperature by placing the resonator in a temperature controlled feedback loop. In this case, the temperature is measured on, or in close vicinity of the resonator. This temperature is then stabilized by heating the resonator to a preset temperature.
An alternative approach is to design the resonator to reduce the dependency of the frequency on temperature. One approach is to combine mono-crystalline silicon with amorphous SiO2, since the Young's modulus of SiO2 exhibits an opposite temperature dependency to that of silicon.
The most straightforward way of combining Si and SiO2 into one resonating body is to grow a layer of oxide on the surface of the Si by means of thermal oxidation.
A schematic process flow is depicted in FIG. 1.
The process starts with a Silicon-on-Insulator (SOI) wafer, comprising a monocrystalline silicon substrate 10, SiO2 layer 12 and silicon layer 14 as shown in FIG. 1A.
The top silicon layer is then patterned as shown in FIG. 1B, followed by an isotropic sacrificial layer etch of the SiO2 layer as shown in FIG. 1C. During the last step the freestanding Si beam 16 element is oxidized in a furnace to provide an oxidised surface layer 18 as shown in FIG. 1D.
After the silicon resonator has been released from the substrate, the exposed parts of the Si surface are covered with a layer of SiO2 by this oxidation process. In order to have perfect temperature compensation, the layer thickness of the Si and SiO2 layers needs to be matched to a high degree. This can be illustrated by considering a disk shaped Si resonator that is covered by layer of SiO2 and is resonating in a radial direction.
The temperature drift of one-eighth of the layout of a 26 MHz disk resonator has been simulated (as a result of symmetry considerations) using finite element modelling. The disk comprises an 80 μm radius disk, with a top layer of SiO2 and a bottom layer of Si. FIG. 2 shows the relative change in temperature drift, as a function of relative change in Si and SiO2 thickness. The relative change in thickness can be considered to be the result of manufacturing tolerances. The scales are relative, so that they represent deviation from a desired thickness. The temperature drift is shown for the Si thickness and for the SiO2 thickness as different plots.
It can be seen that a layer thickness variation smaller than around +1-0.5% (+/−0.005 on the x-axis) is required to meet the GSM specification for temperature drift of +/−0.2 ppm/K (+/−2×10−7 on the y-axis). However, in practice the layer thickness of both the Si and SiO2 layers cannot be controlled better than +/−10% due to manufacturing tolerances. Hence the temperature drift can only be reduced by about a factor 10 compared to a non-oxidized resonator.